Anya and Bill's Deck Painting Problem

Anya and Bill stained a porch deck together in 8 hours. Anya did it alone last year, and Bill took twice as long as Anya the year before. The video defines variables A and B for the hours Anya and Bill take individually. It sets up equations based on their combined rate and Bill's time being twice Anya's. Solving these equations reveals Anya takes 12 hours and Bill 24 hours alone. The video concludes by verifying the solution, showing that together they take less time than individually.

How long did it take Anya and Bill to stain the porch deck together?

• 8 hours

• 12 hours

• 6 hours

• 10 hours

Tags

CCSS.6.EE.C.9

If Bill took twice as long as Anya to paint the deck alone, what relationship can we establish between their times?

• A = 2B

• B = 2A

• B = A/2

• A = B

Tags

CCSS.8.EE.B.5

What does the variable A represent in the context of this problem?

• The number of decks Bill can paint in an hour

• The number of hours Bill takes to paint a deck

• The number of hours Anya takes to paint a deck

• The number of decks Anya can paint in an hour

Tags

CCSS.HSA.CED.A.1

What equation represents the combined work rate of Anya and Bill?

• 8 = 1/A + 1/B

• 1/8 = A + B

• 1/8 = 1/A + 1/B

• 8 = A + B

Tags

CCSS.6.EE.C.9

What is the value of B in terms of A?

• B = A

• B = 2A

• B = A/2

• B = A + 2

Tags

CCSS.HSA.CED.A.1

How many hours does it take Anya to paint the deck alone?

• 8 hours

• 10 hours

• 14 hours

• 12 hours

Tags

CCSS.HSA.CED.A.1

How many hours does it take Bill to paint the deck alone?

• 24 hours

• 20 hours

• 28 hours

• 16 hours

Tags

CCSS.HSA.CED.A.1

What is the significance of the equation 1/8 = 1/A + 1/B?

• It shows the individual work rates of Anya and Bill.

• It calculates the total time taken by Anya and Bill together.

• It represents the combined work rate of Anya and Bill.

• It determines the efficiency of Anya and Bill working alone.

Tags

CCSS.HSA.CED.A.1

Why does it make sense that Anya and Bill take less time together than individually?

• Because they work at the same rate.

• Because their combined efficiency is higher.

• Because they take breaks when working alone.

• Because Bill is more efficient than Anya.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

What conclusion can be drawn about Bill's efficiency compared to Anya's?

• Bill's efficiency does not affect the outcome.

• Bill and Anya are equally efficient.

• Bill is less efficient than Anya.

• Bill is more efficient than Anya.

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9